Glasses containing Al2O3, Ga2O3, and Bi2O3with Li2O have been prepared by twin roller quenching. These glasses are found to exhibit reasonably high ionic conductivities and low electronic conductivities for Li2O concentrations exceeding 50 mole %. The conductivity increases rapidly with increasing Li2O content but does not differ greatly from system to system despite the large difference in the ionic radii of the trivalent cations, Al3+, Ga3+, and Bi3+. A simple model for the behavior is discussed.